Individuals can eat most squashes during all four phases of the Atkins diet. Official Atkins guidelines list summer squash, spaghetti squash, zucchini and pumpkin as acceptable foods during phase 1, the most restrictive phase. Don't eat acorn squash, which has a higher carb count, until phase 3.
The New Health Guide explains that squashes have a medium carbohydrate content, higher than leafy veggies such as spinach but lower than starchy veggies such as potatoes. Acorn squash is starchy, but most other squashes count as foundational vegetables, which are essential in every phase.
Although squashes are vegetables, they're also technically fruits because they contain the plant's seeds. Most nonsweet fruits have moderate carb levels, according to the New Health Guide.